Maximum Likelihood Detection for Cooperative Molecular Communication

Cooperative communication technique is an emerging trend in communication systems and offers benefits of multiple-input-multiple-output (MEMO) systems. Decode-and-forward (DF) method is one of most the known methods that is utilized in cooperative communication systems. Its lower complexity and higher practicality benefits make DF very useful. However, DF is affected negatively by erroneous transmission and performance could be limited. Several approaches are proposed for this drawback. An effective solution is a maximum likelihood (ML) detector that is based on maximization of probability density function in orthogonal transmissions. In this study, ML detector is utilized with orthogonal frequency division multiple access (OFDMA) technique and performance are measured by using software defined radio (SDR) nodes. In order to further improve that solution, a low complex suboptimal detector based on ML detector is proposed. The performance of the suboptimal detector is also quantified with SDR nodes.

In this paper, we design an implementation of a kind of reduced-complexity maximum likelihood (ML) detector for spatial modulation (SM) deployed in a multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) system. Based on National Instruments Universal Software Radio Peripheral (NI USRP) platform, two USRP Reconfigurable Input / Output (USRP-RIO) devices are used as the transmitter and the receiver. Error performance comparisons between the reduced-complexity ML detector and conventional ML detector are made in an indoor environment, as well as the comparison between SM scheme and space-frequency block code (SFBC) scheme. 6 different pictures are exploited as transmitted data, and are reconstructed in the receiver side, so the performance of each scheme is taken on the reconstructed pictures. Both of the calculated bit error ratio (BER) and the reconstruction result of each transmitted pictures, validate the highly consistent error performance of HL_ML detector and conventional ML detector, as well as the error performance superiority of SM over SFBC.

In this paper, we consider the optimal design of linear space codes for an indoor multiple input multiple output (MIMO) visible light communication (VLC) system with maximum-likelihood (ML) detection, where we assume that the full knowledge of channel state information (CSI) is available at both the transmitter and the receiver. For such a system with on-off-keying (OOK) modulation, an optimal closed-form linear space code that maximizes the minimum Euclidean distance for ML detection is attained for the scenario with two transmitters and multiple receivers. Our results reveal the fact that when the channel is good, the optimal code has either a diagonal or an anti-diagonal structure, and when the channel is bad, the optimal code is to diagonalize the channel matrix first, then, optimally distribute the total transmission power into each eigen-subchannel, and then, follow a repetition coding (RC) scheme. Computer simulations verify both the accuracy and the validity of our theoretical analysis, and show that our newly proposed linear space code provides significant error performance gains over currently available space modlution (SM) and RC in literature without CSI at the transmitter.

Orthogonal space-time block codes (OSTBCs) have attracted much attention owing to their simple code construction, maximal diversity gain, and low maximum-likelihood (ML) detection complexity when channel state information (CSI) is available at the receiver. This paper addresses the problem of ML OSTBC detection with unknown CSI. Focusing on the binary and quaternary PSK constellations, we show that blind ML OSTBC detection can be simplified to a Boolean quadratic program (BQP). From an optimization viewpoint the BQP is still a computationally hard problem, and we propose two alternatives for dealing with this inherent complexity. First, we consider the semidefinite relaxation (SDR) approach, which leads to a suboptimal, but accurate, blind ML detection algorithm with an affordable worst-case computational cost. We also consider the sphere decoding approach, which leads to an exact blind ML detection algorithm that remains computationally expensive in the worst case, but generally incurs a reasonable average computational cost. For the two algorithms, we study implementation methods that can significantly reduce the computational complexity. Simulation results indicate that the two blind ML detection algorithms are competitive, in that the bit error performance of the two algorithms is almost the same and is noticeably better than that of some other existing blind detectors. Moreover, numerical studies show that the SDR algorithm provides better complexity performance than the sphere decoder in the worst-case sense, and vice versa in the average sense.

Relay-assisted cooperative free space optical (FSO) communication system is a powerful technique, which offers advantages like fading mitigation and significant gain in spatial diversity due to shorter transmission hops. Even so, it can be hampered by jamming activities which in turn degrade the overall system performance. In this paper, the effect of relay jamming in the decode-and-forward (DF) protocol based cooperative FSO communication system, is introduced and studied thoroughly. The probability density function (pdf) of a random variable containing mixture of the negative exponential and Gaussian random variables is derived. The error performance of the considered FSO system is analysed over this new kind of additive mixture noise for different probabilities of jamming. By utilizing the derived pdf, a closed-form expression of the average bit error rate (BER) of the DF FSO relaying is obtained. A comparison of the BER performance of maximum-likelihood (ML) detector and a derived threshold based detector is also provided. It is observed that the derived threshold based detector offers almost similar performance as that of the ML detector. A thorough numerical study is also provided by considering different pointing error parameters of jammer's and user's channels.

In this paper, we present three new detection schemes for the nonorthogonal amplify and forward (NAF) protocol in a cooperative diversity system based on a multiuser detection approach, namely, a channel inversion type detector, a maximal-ratio combining (MRC) type detector, and a biased maximum likelihood (ML) detector. The decision variables in these schemes are linear functionals of the transmitted symbol vector and therefore they are termed as ldquolinearrdquo detectors. A cooperative relay network using the NAF protocol with N - 1 relays is considered where the source transmits symbols in N - 1 blocks of two time slots in a Rayleigh fading environment. For the case of a general linear space-time block coding scheme using K symbols, we present the performance of this protocol in terms of the code symbol error probability when the symbols come from an M-ary phase-shift keying constellation. The approach is further extended to the transmission in N - 1 blocks of L time slots. Numerical results show that the performance of the MRC type detector is superior to that of the channel inversion type detector, while the biased ML detector has the best performance. However, the MRC type detector has the lowest complexity while the biased ML detector the highest.

Generalized space shift keying (GSSK) proposed for large scale MIMO systems promises significant advantages in terms of hardware costs. However, the maximum likelihood (ML) detection for GSSK is computationally intractable. Detection schemes using compressive sensing (CS) offer a favorable performance-complexity tradeoff. In this letter, we propose a novel GSSK detection framework, where CS algorithms are used to reduce the complexity of ML detection. The proposed framework significantly reduces the performance gap between existing CS-based detection schemes and ML detection while retaining the complexity advantage of CS algorithms. Simulation results demonstrate the superiority of proposed scheme over popular CS-based detection schemes.

Recently, a maximum likelihood (ML) detection rule for differential unitary space time modulation (DUSTM) under the existence of unknown carrier frequency offset (CFO) has been derived. However, the ML detection is based on the exhaustive search over all the unitary group codes. In this paper, we design an efficient detection algorithm for newly derived ML rule, by modifying the bound intersection detector (BID). Our proposed algorithm is seen as a generalization of the existing BID that is known to be an optimal detector for the conventional DUSTM. The simulation results show that the proposed algorithm can save a large portion of the computational complexity compared to the naive searching method.

In order to establish the optimal receiver strategy, in terms of error rate for Single Input Multi Output (SIMO) wireless channels, the Maximum Likelihood (ML) detection should be performed following a multi-dimensional matched filter. However, the implementation of the matched filter and the ML detection both need the estimation of the channel impulse response in advance. In this work, we propose a novel method to establish the matched filters of the SIMO channel blindly alongside a three-step technique for the blind and adaptive ML detection of the symbol vector. With the use of the novel method, the system will benefit from the bandwidth efficiency point of view due to the use of blind schemes. The constant modulus algorithm is utilized to perform the blind matched filtering operation and later Least Mean Squared algorithm is introduced for further correction on the matched filter estimate. The blindly estimated matched filters are incorporated into the ML detector so that the transmitted symbols are found and therefore the channel is equalized. Simulations are provided to present the equalization performance and convergence speed of the novel technique.

In full-duplex orthogonal frequency-division multiplexing systems with IQ imbalances, a frequency-domain least-squares (FD-LS) channel estimator is proposed to estimate both source-to-destination (intended) and destination-to-destination (self-interference) channels. Subsequently, an optimal closed-form pilot matrix is derived to minimize the sum of mean square errors (sum-MSE) of the proposed FD-LS channel estimator. Then, an improved FD-LS estimator is presented and proved to further improve the performance of the FD-LS by exploiting the time-domain property of the channel. In the presence of channel estimation error, an optimal low-complexity maximum likelihood (ML) detector is developed by using eigenvalue and singular value decompositions and whitening the residual self-interference plus noise. Simulation results show that given the proposed FD-LS estimator, the optimal pilot matrix performs much better than those nonsingular pilot matrices with larger conditional numbers (CN). To be specific, the former achieves about 10-dB signal-to-noise ratio (SNR) gain over the latter with CN = 10, the improved FD-LS channel estimator provides about 6-dB SNR gain over the FD-LS estimator at a fixed bit error rate (BER), and the proposed whitening-filter ML detector performs at least 0.6 dB better than the conventional ML detector at a given BER of $10^{-3}$ in the medium-and high-SNR regions.

In this paper, we consider a precoder selection criterion for the maximum-likelihood (ML) detector in limited feedback spatial multiplexing systems. When the ML detector is employed, the exhaustive search for the optimal precoder selection requires very high computational complexity. As a good compromise, we propose a simple precoder selection scheme for the ML detector. It reduces the computational complexity significantly with negligible performance degradation. For the wideband OFDM systems, we extend the precoder selection by introducing a clustering concept in selecting the optimal precoder. Numerical results show that the proposed scheme achieves both the diversity order of the ML detector and the performance enhancement of the limited feedback spatial multiplexing. Moreover, the proposed precoder selection algorithm based on the clustering approach provides enhanced performance compared with conventional interpolation and clustering algorithms.

Multiuser detectors for direct-sequence code-division multiple-access (DS-CDMA) systems based on a recursive convex programming (RCP) relaxation approach are proposed. In these detectors, maximum likelihood (ML) detection is carried out in two steps: first, the combinatorial problem associated with ML detection is relaxed into a convex programming problem and then a recursive approach is applied to get an approximate solution for ML detection. Computer simulations demonstrate that the bit-error rate performance offered by the new detectors is near-optimal and superior to that offered by many existing suboptimal detectors including some recently proposed semidefinite-programming relaxation (SDPR) detectors. In addition, the amount of computation required by the RCP detectors is much less than that required by SDPR detectors.

A low complexity maximum likelihood (ML) detection method is proposed for the square quadrature amplitude modulation (QAM) constellation. In order to reduce the implementation complexity of ML detection, set-partition, subset-selection, and subset-shift are recursively applied to the square QAM constellation. The estimated square QAM symbol is finally given in a closed form as a function of the received signal and the estimated channel. Complexity analysis and numerical simulation confirm that the proposed detection method reduces the implementation complexity substantially and achieves exactly the same performance as the conventional ML detection irrespective of the channel estimation error.

Spatial modulation (SM) is a transmission scheme that uses multiple transmit antennas but only one transmit RF chain. At each time instant, only one among the transmit antennas will be active and the others remain silent. The index of the active transmit antenna will also convey information bits in addition to the information bits conveyed through modulation symbols. Pseudo-random phase precoding (PRPP) is a technique that can achieve high diversity orders even in single antenna systems without the need for channel state information at the transmitter and transmit power control. In this paper, we exploit the advantages of both SM and PRPP simultaneously. We propose a pseudo-random phase precoded SM (PRPP-SM) scheme, where both the modulation bits and the antenna index bits are precoded by pseudo-random phases. The proposed PRPP-SM system gives significant performance gains over SM system without PRPP and PRPP system without SM. Since maximum likelihood (ML) detection becomes exponentially complex in large dimensions, we propose a low complexity local search based detection (LSD) algorithm suited for PRPP-SM systems with large precoder sizes. Our simulation results show that with 4 transmit antennas, 1 receive antenna, 5 × 20 pseudo-random phase precoder matrix and BPSK modulation, the performance of PRPP-SM using ML detection is better than SM without PRPP with ML detection by about 9 dB at 102 BER. This performance advantage gets even better for large precoding sizes. We also propose a precoder index modulation (PIM) scheme, which conveys additional information bits through the choice of a precoding matrix among a set of pre-determined PRPP matrices. Finally, combining the PIM and PRPP-SM schemes, we propose a PIM-SM scheme which conveys bits through both antenna index as well as precoder index.

In this paper, a common framework for maximum likelihood (ML) detection of spatial multiplexed (SM) and space time coded multiple-input multiple-output (MIMO) signals is proposed. It facilitates a common field programmable gate array (FPGA) based hardware design for the detection of both SM and space time block coded (STBC) MIMO signals with reduced computational complexity. We reduce the number of multipliers required for the ML detection by utilizing a set of precomputed combinations of the constellation symbols from lookup tables (LUT) without any degradation in the packet error rate (PER) performance. The reduction in the computational complexity is achieved by using the additional memory that is available in the FPGA. To evaluate the performance of the proposed method, we perform simulations for the WLAN system based on IEEE 802.11 standard using SM-MIMO and STBC-MIMO.